Did you try using a pair of long nose pliers to squeeze the links together? I'm not if KMC's fall into this but some links have a bit of a snap action when installed, and it takes a bit of force to push the links together so you can remove them.

BTW- don't forget that you have to squeeze the links from the rollers, so the plates can slide up. Also some links require that the chain be set in a Z-bend before the links can be removed. If this applies to your link, that may be your problem. Set the link vertical with one the upper chain going right, and the lower going left, then squeeze upward to release.

I have a KMC link and it works just like my Powerlinks, squeeze both ends and it pops out. If yours is dirty then this action is harder to make happen. As far as a 9sp link on a 10 speed chain, not sure. The only obvious difference I can think of is the 10 speed is narrower. It wouldn't seem like that would make any difference in getting it off, but they do make different links for 8 and 9 speeds. Hmmm...

I've had three KMC missing links with their chains but I've never been able to open them with or without pliers EVER. I just use an old powerlink each time, works perfectly for me every time, even by hand on the trail. In fact I just prefer SRAM chains anyhow, but some shops go out of stock.

Park makes a tool for this. I believe it is called the MLP-1.
While it is not normally needed for most links, it does come in handy for some tough ones, such as the sram 10spd links.
The KMC links shouldn't be too hard.
The KMC and SRAM links are pretty tough to get undone when they are brand new, but once ridden a little bit they settle in and usually come off really easily.

Am I just lucky with Powerlinks and the KMC links? I never, ever, never have any issue releasing them by hand. As a check I just walked to the garage and released my KMC on my 9speed xtr chain in 2 seconds.
I'm always amazed at all the problems I read about. I think the biggest thing is mud/dirt in the link. I rarely if ever have that problem.